Solve {l}{x=y+2z}{3x-z=7}{3z-y=7}

$$\left\{ \begin{array} { l } { x = y + 2z } \\ { 3 x - z = 7 } \\ { 3 z - y = 7 } \end{array} \right.$$

Solve for x, y, z

$$x=3$$

$$y=-1$$

$$z=2$$

Short Steps Using Substitution

Substitute y+2z for x in the equation 3x-z=7.

$$3\left(y+2z\right)-z=7$$

Solve the second equation for y and the third equation for z.

$$y=\frac{7}{3}-\frac{5}{3}z z=\frac{7}{3}+\frac{1}{3}y$$

Substitute \frac{7}{3}-\frac{5}{3}z for y in the equation z=\frac{7}{3}+\frac{1}{3}y.

$$z=\frac{7}{3}+\frac{1}{3}\left(\frac{7}{3}-\frac{5}{3}z\right)$$

Solve z=\frac{7}{3}+\frac{1}{3}\left(\frac{7}{3}-\frac{5}{3}z\right) for z.

$$z=2$$

Substitute 2 for z in the equation y=\frac{7}{3}-\frac{5}{3}z.

$$y=\frac{7}{3}-\frac{5}{3}\times 2$$

Calculate y from y=\frac{7}{3}-\frac{5}{3}\times 2.

$$y=-1$$

Substitute -1 for y and 2 for z in the equation x=y+2z.

$$x=-1+2\times 2$$

Calculate x from x=-1+2\times 2.

$$x=3$$

The system is now solved.

$$x=3 y=-1 z=2$$